log以18为底数9为对数=a,18^b=5,求logYI以36为底数45为对数=? 方程log以3为底以(x^2-10)为对数=1 log以三为底以x为对数的解?!!!
1)方法一：log18 9=lg9/lg18=lg9/(lg9 lg2)=alog918=1 lg2/lg9=1/a,lg2=(1/a-1)lg9log18 5=lg5/lg18=lg5/(lg9 lg2)=lg5/(1/a)lg9=blg5=blg9/alog36 45=lg45/lg36=(lg5 lg9)/(2lg2 lg9)=(1 b/a)lg9/(2/a-1)lg9=(a b)/(2-a)方法二：log36 45=log18 45/log18 36=(log18 5 log18 9)/(log18 4 log18 9)log18 9=a,log18 5=blog18 4=log1...全部
1)方法一：log18 9=lg9/lg18=lg9/(lg9 lg2)=alog918=1 lg2/lg9=1/a,lg2=(1/a-1)lg9log18 5=lg5/lg18=lg5/(lg9 lg2)=lg5/(1/a)lg9=blg5=blg9/alog36 45=lg45/lg36=(lg5 lg9)/(2lg2 lg9)=(1 b/a)lg9/(2/a-1)lg9=(a b)/(2-a)方法二：log36 45=log18 45/log18 36=(log18 5 log18 9)/(log18 4 log18 9)log18 9=a,log18 5=blog18 4=log18 (36/9)=log18 (36x9)/(9x9)=log18 18^2/9^2=2-2log18 9=2-2a故log36 45=(log18 5 log18 9)/(log18 4 log18 9)=(a b)/(2-2a a)=(a b)/(2-a)2)log3 (x^2-10)=1 log3 x即log3 (x^2-10)=log3 3 log3 x亦即log3 (x^2-10)=log3 3x故x^2-10=3 x即x^2-3 x-10=0x=5或x=-2(舍去）。
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